Siegert pseudostates: completeness and time evolution

Within the theory of Siegert pseudostates, it is possible to accurately calculate bound states and resonances. The energy continuum is replaced by a discrete set of states. Many questions of interest in scattering theory can be addressed within the framework of this formalism, thereby avoiding the need to treat the energy continuum. For practical calculations it is important to know whether a certain subset of Siegert pseudostates comprises a basis. This is a nontrivial issue, because of the unusual orthogonality and overcompleteness properties of Siegert pseudostates. Using analytical and numerical arguments, it is shown that the subset of bound states and outgoing Siegert pseudostates forms a basis. Time evolution in the context of Siegert pseudostates is also investigated. From the Mittag-Leffler expansion of the outgoing-wave Green's function, the time-dependent expansion of a wave packet in terms of Siegert pseudostates is derived. In this expression, all Siegert pseudostates--bound, antibound, outgoing, and incoming--are employed. Each of these evolves in time in a nonexponential fashion. Numerical tests underline the accuracy of the method

Theory of x-ray absorption by laser-dressed atoms

An ab initio theory is devised for the x-ray photoabsorption cross section of atoms in the field of a moderately intense optical laser (800nm, 10^13 W/cm^2). The laser dresses the core-excited atomic states, which introduces a dependence of the cross section on the angle between the polarization vectors of the two linearly polarized radiation sources. We use the Hartree-Fock-Slater approximation to describe the atomic many-particle problem in conjunction with a nonrelativistic quantum-electrodynamic approach to treat the photon-electron interaction. The continuum wave functions of ejected electrons are treated with a complex absorbing potential that is derived from smooth exterior complex scaling. The solution to the two-color (x-ray plus laser) problem is discussed in terms of a direct diagonalization of the complex symmetric matrix representation of the Hamiltonian. Alternative treatments with time-independent and time-dependent non-Hermitian perturbation theories are presented that exploit the weak interaction strength between x rays and atoms. We apply the theory to study the photoabsorption cross section of krypton atoms near the K edge. A pronounced modification of the cross section is found in the presence of the optical laser.Comment: 13 pages, 3 figures, 1 table, RevTeX4, corrected typoe

Topology optimization of geometrically nonlinear structures using an evolutionary optimization method

Iso-XFEM method is an evolutionary optimization method developed in our previous studies to enable the generation of high resolution topology optimised designs suitable for additive manufacture. Conventional approaches for topology optimization require additional post-processing after optimization to generate a manufacturable topology with clearly defined smooth boundaries. Iso-XFEM aims to eliminate this time-consuming post-processing stage by defining the boundaries using isovalues of a structural performance criterion and an extended finite element method (XFEM) scheme. In this paper, the Iso-XFEM method is further developed to enable the topology optimization of geometrically nonlinear structures undergoing large deformations. This is achieved by implementing a total Lagrangian finite element formulation and defining a structural performance criterion appropriate for the objective function of the optimization problem. The Iso-XFEM solutions for geometrically nonlinear test-cases implementing linear and nonlinear modelling are compared, and the suitability of nonlinear modelling for the topology optimization of geometrically nonlinear structures is investigated

Properties of metastable alkaline-earth-metal atoms calculated using an accurate effective core potential

The first three electronically excited states in the alkaline-earth-metal atoms magnesium, calcium, and strontium comprise the (nsnp) triplet P^o_J (J=0,1,2) fine-structure manifold. All three states are metastable and are of interest for optical atomic clocks as well as for cold-collision physics. An efficient technique--based on a physically motivated potential that models the presence of the ionic core--is employed to solve the Schroedinger equation for the two-electron valence shell. In this way, radiative lifetimes, laser-induced clock shifts, and long-range interaction parameters are calculated for metastable Mg, Ca, and Sr.Comment: 13 pages, 9 table

Influence of preload and nonlinearity of railpads on vibration of railway tracks under stationary and moving harmonic loads

In railway track dynamics, the stiffness and damping properties of railpads have a significant effect on track vibration, decay rates as well forces transmitted to the track supporting structure. Many studies have shown that railpads exhibit pronounced nonlinear behaviour, with preload and frequency dependent properties. This paper presents a three parameter railpad model, together with its differential equation of motion and the required model parameters obtained from experimental data. A time domain model of a rail discretely supported on these railpads is then formulated using the finite element method. The model is subjected to static and dynamic loading in order to study the effects of preload and frequency on its dynamic behaviour. Results are shown as time histories and frequency spectra for the track displacements and reaction forces for various preload levels. They emphasise the necessity of accounting for nonlinear behaviour based on the large disparities (up to 20 dB) observed between the linear and nonlinear cases for the parameters used in this study

Spin configurations in circular and rectangular vertical quantum dots in a magnetic field: Three-dimensional self-consistent simulation

The magnetic field dependence of the electronic properties of \textit{real} single vertical quantum dots in circular and rectangular mesas is investigated within a full three-dimensional multiscale self-consistent approach without any {\it \'a priori} assumptions about the shape and strength of the confinement potential. The calculated zero field electron addition energies are in good agreement with available experimental data for both mesa geometries. Charging diagrams in a magnetic field for number of electrons up to five are also computed. Consistent with the experimental data, we found that the charging curves for the rectangular mesa dot in a magnetic field are flatter and exhibit less features than for a circular mesa dot. Evolution of the singlet-triplet energy separation in the two electron system for both dot geometries in magnetic field was also investigated. In the limit of large field, beyond the singlet-triplet transition, the singlet-triplet energy difference continues to become more negative in a circular mesa dot without any saturation within the range of considered magnetic fields whilst it is predicted to asymptotically approach zero for the rectangular mesa dot. This different behavior is attributed to the symmetry "breaking" that occurs in the singlet wave-functions in the rectangular mesa dot but not in the circular one.Comment: 12 pages, 8 gifure

Pseudo-dynamic method for structural analysis of automobile seats

This work describes the application of a pseudo-dynamic (PsD) method to the dynamic analysis of passenger seats for the automotive industry. The project of such components involves a structural test considering the action of dynamic forces arising from a crash scenario. The laboratory certification of these automotive components consists essentially on the inspection of the propagation and extension of plastic deformations zones in metallic members of the seat structure as consequence of the mutual action between the seat and the passenger fastened to the seat via seat belt anchorages. This work presents a relatively simple experiment using PsD techniques as a novel method to performa test equivalent to the dynamic model of a dummy-seat pair subjected to impulsive loads from a car crash. Essentially, the PsD test method is a hybrid and hierarchic computer-driven testing procedure where a numerical algorithm and experimental step are used and combined on-line in order to solve a problem in the scope of structural dynamics. The implementation of the method is not expensive and has the leading advantage of offering the operator a total control of any intermediate structure state during the test still keeping the realism of a real dynamic testing.Project: NDT-AUTO Ref 13-02-2003-FDR-01281 (Agencia de Inovação

Development of Flutter Constraints for High-fidelity Aerostructural Optimization

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143080/1/6.2017-4455.pd

Mode tracking issues in structural optimization

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76633/1/AIAA-12747-342.pd

A Nonrigid Registration Method for Correcting Brain Deformation Induced by Tumor Resection

Purpose: This paper presents a nonrigid registration method to align preoperative MRI with intraoperative MRI to compensate for brain deformation during tumor resection. This method extends traditional point-based nonrigid registration in two aspects: (1) allow the input data to be incomplete and (2) simulate the underlying deformation with a heterogeneous biomechanical model. Methods: The method formulates the registration as a three-variable (point correspondence, deformation field, and resection region) functional minimization problem, in which point correspondence is represented by a fuzzy assign matrix; Deformation field is represented by a piecewise linear function regularized by the strain energy of a heterogeneous biomechanical model; and resection region is represented by a maximal simply connected tetrahedral mesh. A nested expectation and maximization framework is developed to simultaneously resolve these three variables. Results: To evaluate this method, the authors conducted experiments on both synthetic data and clinical MRI data. The synthetic experiment confirmed their hypothesis that the removal of additional elements from the biomechanical model can improve the accuracy of the registration. The clinical MRI experiments on 25 patients showed that the proposed method outperforms the ITK implementation of a physics-based nonrigid registration method. The proposed method improves the accuracy by 2.88 mm on average when the error is measured by a robust Hausdorff distance metric on Canny edge points, and improves the accuracy by 1.56 mm on average when the error is measured by six anatomical points. Conclusions: The proposed method can effectively correct brain deformation induced by tumor resection. (C) 2014 American Association of Physicists in Medicine